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Mathematical Reasoning course

  1. May 13, 2013 #1
    Hey guys, I just recently transferred to the mathematics department at University of Illinois as a junior undergrad and one of the classes I'm required to take this fall is called Mathematical Reasoning and I'm pretty sure it has to do with proofs... Which I know absolutely nothing about! What is a good resource (book, video, website) where I can start learning this stuff from ground 0?
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  3. May 15, 2013 #2
    I think that the best way to learn mathematical reasoning is to just choose any topic that you find interesting and read rigerous textbooks for that topic.

    If you are interested in calculus I would suggest "ISBN: 9780387904597 Elementary analysis : the theory of calculus, Author: Kenneth A. Ross."

    If you are interested in Algebra I would suggest "Introduction to Abstract Algebra, by Neal H. McCoy and Gerald J. Janusz ISBN: 9780982263310"
  4. May 15, 2013 #3


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  5. May 16, 2013 #4
    Thank you for the replies guys! Also thanks to the moderator for moving my thread, greatly appreciated :D

    I will check out the links to both books and try to get a head start on this subject before fall classes start. I'm worried about the class, a lot :((, I have no experience in this area whatsoever. I did just fine in calculus and differential equations... but they kind of work off one another. This seems like a totally different area of maths.
  6. May 16, 2013 #5


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    Don't worry about it. Just study the definitions carefully and do a lot of simple-looking exercises, and you'll do fine.
  7. May 23, 2013 #6
    I just finished a junior level course in mathematical proofs. We used the 3rd edition of this book: https://www.amazon.com/s/ref=nb_sb_...hematics&sprefix=mathematical+proofs,aps,1188 . I purchased the 2nd edition to save money, and comparing side-by-side, the two editions aren't that different. It reads relatively easily, and has sections on logic, truth tables, logical equivalence, direct proofs, proof by contradiction, minimum counter example proofs, induction, strong induction. Our class mostly did number theory to focus on the methods of proofs, other professors just into a couple new advanced topics (e.g. rings) and they learn how to prove along the way.

    A discrete math text would also be worth looking into for logic, and goodwillbooks.com will probably have one that you can get to your door for less than $5.
    Last edited by a moderator: May 6, 2017
  8. May 23, 2013 #7
  9. May 23, 2013 #8
    Thank you so much to everyone, I cannot tell you how much this helps and encourages me :D **mr bean style thumbs up** lol
  10. May 25, 2013 #9
    I learned what proving something "meant" by reading Spivak's Calculus and doing the exercizes. Then comparing my solutions to the one's in the solution manuel (I had no teacher).
  11. May 30, 2013 #10
    Has anyone ever used the Demystified series Math Proofs? I'm currently using that book to get started because all the other suggestions are damn hard to follow at the moment. I was wondering if anyone can tell me if I'm just wasting my time with this book?
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